Probing the axion-electron coupling at cavity experiments

Axion dark matter induces electromagnetic radiation in conductors through nearly perpetual oscillations of electrons, driven by axion-electron interactions through the so-called chiral magnetic effect. It therefore provides a complementary probe of the axion-electron coupling $g_{ae}$ beyond the conventional axion-photon coupling $g_{a \gamma}$ in cavities. We show that existing axion cavity experiments can constrain the coupling to $g_{ae}\lesssim 10^{-5}$ over the scanned axion mass ranges, $1\,\mu\, {\rm eV}\lesssim m_a\lesssim 20\,\mu\,{\rm eV}$. Although we find that the radiation due to $g_{ae}$ at the copper cavity surface of electric conductivity $\sigma$ is suppressed by $m_a^2/\sigma^2\sim 10^{-20}$, compared to the radiation inside the cavity by the axion-photon conversion due to $g_{a\gamma}$, a sensitivity of about $10^{-9}$ could be achieved for $g_{ae}$ over a wider range of $m_a$, including values higher than those previously probed, if copper walls are replaced with carbon-based conductors.